Appraisal: NPV is the referee
Introduced| English | Meaning |
|---|---|
| net present value/net ˈprezənt ˈvæljuː/ | The value today of future cash flows after subtracting the initial cost. |
| hurdle rate | the minimum return a project must clear, set by the cost of capital |
Three rules, one referee
- The flows are on the table: -60,000 +18,000 +22,000 +26,000 +24,000 +20,000. NPV at 8% = 27,420 ✓; IRR = 23.6% ✓; payback = 2.77 years ✓ (discounted 3.22).
- All three agree here — and finance still insists: The net present value 净现值 (NPV) is the referee, the others are commentary.
The profile tells the truth
- The NPV profile falls with the discount rate and crosses zero once (conventional flows) at IRR 23.6%. Where flows change sign twice, IRR can exist twice — the profile, not the formula, says so.
- The hurdle rate 门槛收益率 is the WACC (9.19%, unit 5): at it, NPV = 23,604.
Flows -60,000 +18,000 +22,000 +26,000 +24,000 +20,000. NPV at 8%, to the nearest pound?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
The inflows discount to 87,420: NPV = 27,420. At the 9.19% WACC, 23,604 - still comfortably positive.
The same project. The IRR, in % (one decimal)?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
At 23.6% the discounted inflows equal 60,000 - where the profile crosses zero.
Payback in years (two decimals)?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
After year 2, 40,000 recovered of 60,000: 2 + 20,000/26,000 = 2.77. Discounted: 3.22.
NPV at the 9.19% WACC, to the nearest pound?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
23,604 - the hurdle moved, the verdict did not. But 3,816 of the earlier NPV was the 8% guess being wrong.
Match each rule to its question.
Difficulty 2/5 · 140 coins + a small bonus on first completion today
Three answers and one cost - quoted together they describe the project honestly.
What each rule answers
- NPV: HOW MUCH richer (pounds today) — the decision. IRR: what RATE (scale-free) — a summary. Payback: how LONG exposed — a liquidity note.
- Ranking by IRR misleads on scale: 50% on 1 pound does not beat 20% on 60,000. Rank mutually exclusive projects by NPV.
Which rule answers which question?
Route each decision question to NPV, IRR or payback - and spot where IRR misleads.
Two mutually exclusive projects. The ranking rule is:
Difficulty 1/5 · 100 coins + a small bonus on first completion today
IRR ignores scale: 50% on 1 pound never beats 20% on 60,000. NPV counts pounds.
A project with -60,000, +140,000, -90,000 flows. What can happen to its IRR?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Two sign changes can produce two crossings - the profile is the honest tool, and NPV still decides.
A 2.77-year payback is sufficient reason to accept the project.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Payback ignores everything after recovery - it is a risk note, never the decision. The NPV decides; the payback informs.
Three appraisal slips
- Ranking by IRR when projects differ in scale or timing.
- Accepting on payback alone - it ignores everything after recovery.
- Quoting IRR without the profile when flows change sign more than once.
Recap
- NPV = value in pounds: decide on it.
- IRR = the profile zero; misleads on scale and multiple crossings.
- Payback = exposure time. Quote all three; decide on NPV.